Jason M. Reese

Fluid Shear Stress Induction of the Tissue Factor Promoter In Vitro and In Vivo Is Mediated by Egr-1

Hemodynamic forces such as fluid shear stress have been shown to modulate the activity of an expanding family of genes involved in vessel wall homeostasis and the pathogenesis of vascular disease. We have investigated the effect of shear stress on tissue factor (TF) gene expression in human endothelial cells (ECs) and in a rat arterial model of occlusion. As measured by reverse transcriptase polymerase chain reaction, exposure of ECs to 1.5 N/m2 shear stress resulted in a time-dependent induction of endogenous TF transcripts of over 5-fold. Transient transfection of TF promoter mutants into cultured ECs suggests the involvement of the transcription factor Egr-1 in mediating the response of the TF promoter to shear stress. To address the importance of flow induction of Egr-1 in vivo, we have established a flow-restricted rat arterial model and determined the level of expressed Egr-1 and TF at the site of restricted flow using immunohistochemistry. We report an increase in the level of Egr-1 and TF protein in ECs expressed at the site of restricted flow. Elevated expression of Egr-1 and TF is restricted to a highly localized area, as evidenced by the fact that no significant increase in level can be detected at arterial sites distal to the site of occlusion. These findings suggest a direct role for Egr-1 in flow-mediated induction of TF and further substantiate the importance of shear stress as a modulator of vascular endothelial gene function in vivo.

The usefulness of higher-order constitutive relations for describing the Knudsen layer

The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC (direct simulation Monte Carlo) data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets (Grads 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions (needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight.

New directions in fluid dynamics: non-equilibrium aerodynamic and microsystem flows

Fluid flows that do not have local equilibrium are characteristic of some of the new frontiers in engineering and technology, for example, high–speed high–altitude aerodynamics and the development of micrometre–sized fluid pumps, turbines and other devices. However, this area of fluid dynamics is poorly understood from both the experimental and simulation perspectives, which hampers the progress of these technologies. This paper reviews some of the recent developments in experimental techniques and modelling methods for non–equilibrium gas flows, examining their advantages and drawbacks. We also present new results from our computational investigations into both hypersonic and microsystem flows using two distinct numerical methodologies: the direct simulation Monte Carlo method and extended hydrodynamics. While the direct simulation approach produces excellent results and is used widely, extended hydrodynamics is not as well developed but is a promising candidate for future more complex simulations. Finally, we discuss some of the other situations where these simulation methods could be usefully applied, and look to the future of numerical tools for non–equilibrium flows.

On the modelling of isothermal gas flows at the microscale

This paper makes two new propositions regarding the modelling of rarefied (nonequilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case. Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier–Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model’s generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers.

The structure of shock waves as a test of Brenner's modifications to the Navier-Stokes equations

Brenner (Physica A, vol. 349, 2005a, b, pp. 11, 60) has recently proposed modifications to the Navier-Stokes equations that are based on theoretical arguments but supported only by experiments having a fairly limited range. These modifications relate to a diffusion of fluid volume that would be significant for flows with high density gradients. So the viscous structure of shock waves in gases should provide an excellent test case for this new model. In this paper we detail the shock structure problem and propose exponents for the gas viscosity-temperature relation based on empirical viscosity data that is independent of shock experiments. We then simulate monatomic gas shocks in the range Mach 1.0-12.0 using the Navier-Stokes equations, both with and without Brenners modifications. Initial simulations showed that Brenners modifications display unphysical behaviour when the coefficient of volume diffusion exceeds the kinematic viscosity. Our subsequent analyses attribute this behaviour to both an instability to temporal disturbances and a spurious phase velocity-frequency relationship. On equating the volume diffusivity to the kinematic viscosity, however, we find the results with Brenners modifications are significantly better than those of the standard Navier-Stokes equations, and broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. Brenners modifications add only two terms to the Navier-Stokes equations, and the numerical implementation is much simpler than conventional extended hydrodynamic models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark non-equilibrium flow cases.

Capturing the Knudsen Layer in Continuum-Fluid Models of Nonequilibrium Gas Flows

In hypersonic aerodynamics and microflow device design, the momentum and energy fluxes to solid surfaces are often of critical importance. However, these depend on the characteristics of the Knudsen layer - the region of local non-equilibrium existing up to one or two molecular mean free paths from the wall in any gas flow near a surface. While the Knudsen layer has been investigated extensively using kinetic theory, the ability to capture it within a continuum-fluid formulation (in conjunction with slip boundary conditions) suitable for current computational fluid dynamics toolboxes would offer distinct and practical computational advantages.

Molecular dynamics in arbitrary geometries: parallel evaluation of pair forces

A new algorithm for calculating intermolecular pair forces in molecular dynamics (MD) simulations on a distributed parallel computer is presented. The arbitrary interacting cells algorithm (AICA) is designed to operate on geometrical domains defined by an unstructured, arbitrary polyhedral mesh that has been spatially decomposed into irregular portions for parallelisation. It is intended for nano scale fluid mechanics simulation by MD in complex geometries, and to provide the MD component of a hybrid MD/continuum simulation. The spatial relationship of the cells of the mesh is calculated at the start of the simulation and only the molecules contained in cells that have part of their surface closer than the cut-off radius of the intermolecular pair potential are required to interact. AICA has been implemented in the open source C++ code OpenFOAM, and its accuracy has been indirectly verified against a published MD code. The same system simulated in serial and in parallel on 12 and 32 processors gives the same results. Performance tests show that there is an optimal number of cells in a mesh for maximum speed of calculating intermolecular forces, and that having a large number of empty cells in the mesh does not add a significant computational overhead.

Velocity slip in microscale cylindrical Couette flow: The Langmuir model

The velocity slip on the solid surfaces of microscale cylindrical Couette flow is investigated using the Langmuir adsorption model for the gas-surface molecular interaction. The accommodation coefficient in the Maxwell model, which is a free parameter based on the concept of diffusive reflection, is replaced by a physical parameter of heat adsorption in the Langmuir model. The phenomenon of velocity inversion is then clearly explained by introducing a velocity polar on the hodograph plane. It is also shown that the quantity used to determine the momentum slip in a concentric cylindrical geometry should be based upon the angular velocity, not the velocity itself. Finally, and despite their totally independent considerations of the gas-surface molecular interaction, the Maxwell and Langmuir slip models are shown to be in qualitative agreement with direct simulation Monte Carlo data in capturing the general features of the flow field.

Controllers for imposing continuum-to-molecular boundary conditions in arbitrary fluid flow geometries

We present a new parallelised controller for steering an arbitrary geometric region of a molecular dynamics (MD) simulation towards a desired thermodynamic and hydrodynamic state. We show that the controllers may be applied anywhere in the domain to set accurately an initial MD state, or solely at boundary regions to prescribe non-periodic boundary conditions (PBCs) in MD simulations. The mean molecular structure and velocity autocorrelation function remain unchanged (when sampled a few molecular diameters away from the constrained region) when compared with those distributions measured using PBCs. To demonstrate the capability of our new controllers, we apply them as non-PBCs in parallel to a complex MD mixing nano-channel and in a hybrid MD continuum simulation with a complex coupling region. The controller methodology is easily extendable to polyatomic MD fluids.

Flow enhancement in nanotubes of different materials and lengths

The high water flow rates observed in carbon nanotubes (CNTs) have previously been attributed to the unfavorable energetic interaction between the liquid and the graphitic walls of the CNTs. This paper reports molecular dynamics simulations of water flow in carbon, boron nitride, and silicon carbide nanotubes that show the effect of the solid-liquid interactions on the fluid flow. Alongside an analytical model, these results show that the flow enhancement depends on the tubes geometric characteristics and the solid-liquid interactions.